If a certain brand of lightbulb has a population mean lifetime of 960
hours and a population standard deviation of 170 hours, what is the
probability that a sample of 50 lightbulbs from this population will
have a sample mean of more than 1000 hours?

Please explain how you arrived at the answer.

Dear danbanker:

From the problem, we know that the population mean lifetime mu is 960
hours and the population standard deviation sigma is 170 hours.

The central limit theorem tells us that the sample mean lifetime has
approximately the N [mu, sigma/square root (n)] distribution where n
is the sample size.  In this case, for a sample of 50, the standard
distribution is 170/square root (50) = 24.04.

Therefore, the probability that we want is P (sample mean lifetime >
1000) = P [(sample mean lifetime - 960)/24.04 > (1000 - 960)/24.04] =
P (Z > 1.66) = 0.0485.

The probability that Z > 1.66 is obtained from a table of standard
normal probabilities such as that found inside the front cover of the
following reference.

Source: "Introduction to the Practice of Statistics" by Moore and
McCabe, W. H. Freeman & Co., 1989

Sincerely,

Wonko